Circles: Tangents at Endpoints of Diameter are Parallel

Let $AB$ be a diameter of a circle with center $O$. Let lines $PQ$ and $RS$ be the tangents drawn to the circle at the endpoints $A$ and $B$ respectively.

Radius is perpendicular to the tangent at the point of contact: $OA \perp PQ \implies \angle PAB = 90^\circ \quad \text{and} \quad \angle QAB = 90^\circ$ $OB \perp RS \implies \angle RBA = 90^\circ \quad \text{and} \quad \angle SBA = 90^\circ$

Notice that $\angle PAB = \angle SBA = 90^\circ$. These are alternate interior angles for lines $PQ$ and $RS$ intersected by transversal $AB$. Since alternate interior angles are equal, $PQ \parallel RS$.